The resolution of an imaging optical system determines the amount of information that can be obtained about the object being viewed. In an ideal imaging system, a point on the object is imaged to a point in the image. As an example, consider a simple telescope designed using geometrical (or ray) optics such that a point object at infinity is focused to a perfect point. See FIG. 1. Because of the wave nature of light, the light in this system will not focus to a geometrical point, but rather will focus to a small spot as shown (magnified) in FIG. 2
In FIG. 2 most of the light is concentrated into a single lobe (centered on the location of the ideal image point) surrounded by concentric rings of decreasing intensity. This pattern, caused by diffraction, is known as the impulse response of the optical system. The width of the central lobe largely determines the resolution of the imaging system. For example, consider two point objects. Each object generates an impulse response having an intensity distribution similar to that shown in FIG. 2. As the separation between the two point objects decreases, the separation between the central lobes of the impulse responses corresponding to each point object also decreases, and the central lobes will eventually overlap at least partially. Thus, as the distance between the two point objects decreases it becomes increasingly difficult for a given imaging system to distinguish between the objects and/or determine that two point objects were present. However, two point objects having relatively narrow central lobes can be resolved at smaller separation distances by the given imaging system since the point objects must be closer together before their relatively narrow central lobes begin to overlap. Thus, the resolution of an imaging system can be increased by reducing the width of the central lobes.
One method of reducing the width of the central lobes is a technique called apodization. Apodization consists of modifying the impulse response of the system by altering the entrance pupil of the imaging system. This can be accomplished by using a mask in which the amplitude and/or phase of the incoming beam is modified. For example, one way to narrow the central lobe of the impulse response of a telescope is to center a circular obstruction in front of or over the entrance pupil of the telescope. A central obstruction which is 90% the size of the entrance pupil of the telescope produces the annular aperture function shown in FIG. 3 and the impulse response shown in FIG. 4 (which also shows the unapodized response).
It is apparent from FIG. 4 that the impulse response of the apodized system has a much narrower central lobe. However, the magnitude of the rings or “feet” surrounding the central lobe increases and the intensity distribution of the impulse response becomes wider relative to the unapodized system. Although the resolution of point objects is enhanced with the use of the central obstruction, extended or non-point objects will appear less distinct. As an example, consider the image of a small, sharp-edged, circular disk. Each point on the object produces a corresponding point on the image having an impulse response with a corresponding intensity distribution. The resulting image is fuzzy around the edges due to the extended and increased-magnitude rings or feet of the wider intensity distribution of the impulse response.
The above analysis is an example of an apodizer that alters the amplitude of the incoming light. It has been shown (refs. [3], [5]) that the width of the central lobe can be reduced at most by a factor of 1.6 using apodizers that alter the amplitude of the light. It is also possible to produce an apodization by altering the phase of the incident light. Using such phase apodizers it has been shown (ref. [4]) that the central lobe can be indefinitely narrowed. However, this extreme is not used in practice because of an increase in intensity of the surrounding light.
Conventional apodizers use square apertures and cross-shaped apodizers, as shown in U.S. Pat. No. 5,249,080, or sawtooth patterns as shown in U.S. Pat. No. 3,977,772, or diffuse, opaque particles as shown in U.S. Pat. No. 4,030,817.